Turbulence suppression and regeneration in a magnetohydrodynamic duct flow due to influence of arbitrary electrically conductive walls

In the current study, we present a series of numerical simulations describing a turbulent magnetohydrodynamic flow subjected to a transverse magnetic field in a square duct with arbitrary electrically conductive walls. The characteristic flow and electromagnetic non-dimensional parameters (Reynolds and Hartmann number, respectively) were fixed, while the wall conductivity ratio (Cd) was varied from the perfectly electrically insulated (Cd = 0) to perfectly electrically conducting (C d → ∞). We have assumed the one-way coupling between the flow of an electrically conducting fluid and the imposed magnetic field. The influence of the electrically conducting walls was imposed by simulating additional finite solid domains coupled with the channel interior. The turbulence was simulated by applying the large eddy simulation approach with the dynamic Smagorinsky sub-grid scale model. The obtained results confirmed a significant impact of the conductivity of the surrounding walls on the flow and turbulence reorganization. We have observed that the initially fully developed turbulence regime was gradually suppressed in the 0 ≤ C d < 0.15 range, while the fully laminarized state was obtained at C d = 0.15. We found that the process of turbulence suppression was accompanied by the appearance of the patterned turbulence phenomenon in the proximity of the walls parallel to the magnetic field direction. With a further increase in the wall conductivity parameter (0.15 < C d < ∞), we have observed a complete turbulence regeneration. We found that this turbulence regeneration was caused by the local reorganization of the total current density loops near the electrically conducting walls.